# Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guarantees

arXiv: https://arxiv.org/abs/2312.01959 · HTML: https://mlsanity.com/paper/2312.01959/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 69 references that are in the map.
- First posted on arXiv 4 Dec 2023.

## Builds on (most cited first, 22 of 22)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [The Probabilistic Model Checker Storm](https://mlsanity.com/paper/2002.07080/) (2020)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [Robust Online Monitoring of Signal Temporal Logic](https://mlsanity.com/paper/1506.08234/) (2015)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [JuliaReach: a Toolbox for Set-Based Reachability](https://mlsanity.com/paper/1901.10736/) (2019)
- [Multi-Agent Reachability Calibration with Conformal Prediction](https://mlsanity.com/paper/2304.00432/) (2023)
- [RTAMT: Online Robustness Monitors from STL](https://mlsanity.com/paper/2005.11827/) (2020)
- [On-Line Monitoring for Temporal Logic Robustness](https://mlsanity.com/paper/1408.0045/) (2014)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Predictive Runtime Monitoring for Mobile Robots using Logic-Based Bayesian Intent Inference](https://mlsanity.com/paper/2108.01227/) (2021)
- [Smoothed Model Checking for Uncertain Continuous Time Markov Chains](https://mlsanity.com/paper/1402.1450/) (2014)
- [Neural Predictive Monitoring under Partial Observability](https://mlsanity.com/paper/2108.07134/) (2021)
- [Neural State Classification for Hybrid Systems](https://mlsanity.com/paper/1807.09901/) (2018)
- [Sampling-Based Verification of CTMCs with Uncertain Rates](https://mlsanity.com/paper/2205.08300/) (2022)
- [Time-Robust Control for STL Specifications](https://mlsanity.com/paper/2104.02677/) (2021)
- [An STL-based Formulation of Resilience in Cyber-Physical Systems](https://mlsanity.com/paper/2205.03961/) (2022)

## Built on by (most cited first, 2 of 2)

- [ProbGuard: Proactive Runtime Monitoring for LLM Agent Safety via Probabilistic Prediction](https://mlsanity.com/paper/2508.00500/) (2025)
- [CoCAI: Copula-based Conformal Anomaly Identification for Multivariate Time-Series](https://mlsanity.com/paper/2507.17796/) (2025)

## Abstract (arXiv)

This tutorial focuses on efficient methods to predictive monitoring (PM), the problem of detecting at runtime future violations of a given requirement from the current state of a system. While performing model checking at runtime would offer a precise solution to the PM problem, it is generally computationally expensive. To address this scalability issue, several lightweight approaches based on machine learning have recently been proposed. These approaches work by learning an approximate yet efficient surrogate (deep learning) model of the expensive model checker. A key challenge remains to ensure reliable predictions, especially in safety-critical applications. We review our recent work on predictive monitoring, one of the first to propose learning-based approximations for CPS verification of temporal logic specifications and the first in this context to apply conformal prediction (CP) for rigorous uncertainty quantification. These CP-based uncertainty estimators offer statistical guarantees regarding the generalization error of the learning model, and they can be used to determine unreliable predictions that should be rejected. In this tutorial, we present a general and comprehensive framework summarizing our approach to the predictive monitoring of CPSs, examining in detail several variants determined by three main dimensions: system dynamics (deterministic, non-deterministic, stochastic), state observability, and semantics of requirements' satisfaction (Boolean or quantitative).